Preheat oven to 375°F. For easy clean-up, line a 15"x10"x1" baking pan with foil. Spray with cooking oil and set aside.
In a large bowl, combine the first 7 ingredients; toss to coat. Place chicken and vegetables in a single layer on baking pan; sprinkle with pepper. Bake until a thermometer inserted in chicken reads 165°F and vegetables are tender, 35-40 minutes.
Preheat broiler with oven rack 3"-4" from heat. Broil chicken and vegetables until lightly browned (2-4 minutes).
Cool slightly and sprinkle with feta cheese.